All Questions
5 questions
6
votes
1
answer
291
views
Example of nice isomorphism between Cl$_{p,q}(\mathbb R)$ and matrix algebras over $\mathbb R,\mathbb C,\mathbb H,\mathbb R^2,\mathbb C^2,\mathbb H^2$
$\DeclareMathOperator\Cl{Cl}$It is known that every Clifford Algebra $\Cl(Q)$ over the real numbers where $Q: \mathbb R^n \to \mathbb R$ is a non-degenerate quadratic form is isomorphic to a matrix ...
- 4,943
8
votes
1
answer
234
views
What is the inverse in K-theory represented by Clifford module extensions?
I am working on a model for topological KO-theory which is represented by explicit spaces of orthogonal Clifford module extensions. That is, assuming $M$ compact, $KO^{-n+1}(M) := [M,X_n]$ where the ...
- 151
1
vote
0
answers
103
views
Which operators constructed from 10d gamma matrices commute with $SO(1,2)\times SO(3)\times SO(3)$?
In the paper Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory by Gaiotto and Witten, an in-depth analysis of boundary conditions in N=4 Super Yang-Mills in four dimensions in ...
- 1,155
5
votes
2
answers
542
views
Explicit Isomorphism between $Cl(8)$ and $\mathbb{R}(16)$
I am looking for a explicit isomorphism between $Cl(8)$ (Clifford algebra over $\mathbb{R}^8$ with standard Euclidean metric) and $\mathbb{R}(16)$ (algebra of $16\times 16$ matrices over $\mathbb{R}$)....
- 2,091
3
votes
1
answer
1k
views
On matrix representations of the Clifford algebras of type $Cl(0,n)$
Can matrix representations of clifford algebras of type Cl(0,n) be found? Specifically for even orders
- 33